Wave Optics

JEE Main level, single correct, medium

50 of 191

Question 50 of 191

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion-(A) : If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer.
Reason-(R) : The speed of light reduces in an optically denser medium than air while its frequency does not change.
In the light of the above statements, choose the most appropriate answer from the options given below :

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Answer: (B) Both (A)(\mathbf{A}) and (R)(\mathbf{R}) are true and (R)(\mathbf{R}) is the correct explanation of (A)(\mathbf{A})

β( fringe width )=λDd\beta(\text { fringe width })=\frac{\lambda D}{d}

In denser medium, λ↓⇒β↓\lambda \downarrow \Rightarrow \beta \downarrow ⇒\Rightarrow fringe come closer

Also, μ=cV⇒V=cμ\mu=\frac{\mathrm{c}}{\mathrm{V}} \Rightarrow \mathrm{V}=\frac{\mathrm{c}}{\mu}
Frequency remains same,
⇒μ=λvac.fλmedf⇒λmed=λvac.μ\Rightarrow \mu=\frac{\lambda_{\mathrm{vac} .} \mathrm{f}}{\lambda_{\mathrm{med}} \mathrm{f}} \Rightarrow \lambda_{\mathrm{med}}=\frac{\lambda_{\mathrm{vac} .}}{\mu}

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